I think this depends on the definition of the term mantra. For example, the term mantra in the context of Vedic Hinduism says that a mantra is only a mantra when it comes from one of the four Vedas, and should always start with om. Everything else is not called a mantra in this type of definition. Then you also have various Buddhist mantras. Another definition of mantra can include bija-mantras japa-mantras, dhyana-mantras etc.
– Gabe HiemstraMar 15 '17 at 11:00

I am noticing that people often downvote answers that are perfectly correct. I think the site should change its rules so that the name of the downvoter is revealed and the downvoter would have to explain the reason for the downvote.
– Pradip GangopadhyayJul 4 '14 at 13:40

I think site should implement a rule that says every downvoter must post a comment and only after that they are allowed to downvote. This way we'll know who that is and the reason. A special icon will be attached to the downvoter's comment so people can differentiate between normal ones and dowvoted ones.
– Chinmay SarupriaMar 15 '17 at 10:22

The mantra is the body.And Pranava OM is the head.When the
body(mantra) and the head(OM) are connected only then the recital(of the mantra) bears fruits.

Also, see this post to know why not only mantras but all Vedic recitals should begin with the pranava OM.

However,as per the Mahanirvana Tantram,which is a Shakta Agama,mantras in Kali Yuga are more effective if preceded by HREEM (the maya beeja) instead of OM.

In the Satya, Treta, and Dvapara Ages, the Mantras, O Kalika! were in
their application preceded by the Pranava (9); but in the Kali Age, O
Supreme Devi! the decree of Shankara is that man do perform all rites
with the aid of the same Mantras, but preceded by the Maya Bija (10).
All Mantras in the Nigamas, Agamas, Tantras, Samhitas and Vedas, have
been spoken by Me. Their employment, however, varies according to the
Ages (11). For the benefit of men of the Kali Age, men bereft of
energy and dependent for existence on the food they eat, the Kula
doctrine, O Auspicious One! is given (12).

Mahanirvana Tantram Chapter 9

NOTE-Hreem is called the maya beeja which is present in many famous Devi mantras.Other some important beejas are Kleem(Kama Beejam) Aim (Vaga Beejam)

Welcome To Hinduism SE! As I have earlier commented on your previous post , You should specifically have to provide link to the mantras you mentioned here , from the web site which you are using for references. Also pls. Confirm that Da Bei zhou Mantra and others are related to Hinduism.Thank You.
– SwiftPushkarAug 30 '16 at 18:21

1

Can you write the Hanuman Mantra ,which you have mentioned in answer , which doesn't start with Om. ॐ हनुमते नमः | Om shree Hanumataye Namah is main mantra.
– SwiftPushkarAug 30 '16 at 18:31